he errors that Lewis and Clark made in latitude and longitude calculations were less the result of their instruments, their mathematics, or field conditions than by small errors of three types that affect all astronomical observations:
(1) miscalculating refraction or the bending of light in the atmosphere, which causes altitudes to appear slightly greater than they actually are;
(2) estimating semidiameter of either the sun or moon, the discs of which are too large to be used entire when making a sighting, making it necessary to sight, for example, the "sun's upper limb" or top half or the "moon's lower limb" or bottom half and then correct by calculation to obtain a reading at the center of the disc; and
(3) correcting for "parallax," the fact that while navigational tables are based on distances and angles calculated from the earth's center, observations are made from the earth's surface.
--John Logan Allen